Physics-Informed Synthetic Dataset and Denoising TIE-Reconstructed Phase Maps in Transient Flows Using Deep Learning

Abstract: High-speed quantitative phase imaging enables non-intrusive visualization of transient compressible gas flows and energetic phenomena. However, phase maps reconstructed via the transport of intensity equation (TIE) suffer from spatially correlated low-frequency artifacts introduced by the inverse Laplacian solver, which obscure meaningful flow structures such as jet plumes, shockwave fronts, and density gradients. Conventional filtering approaches fail because signal and noise occupy overlapping spatial frequency bands, and no paired ground truth exists since every frame represents a physically unique, non-repeatable flow state. We address this by developing a physics-informed synthetic training dataset where clean targets are procedurally generated using physically plausible gas flow morphologies, including compressible jet plumes, turbulent eddy fields, density fronts, periodic air pockets, and expansion fans, and passed through a forward TIE simulation followed by inverse Laplacian reconstruction to produce realistic noisy phase maps. A U-Net-based convolutional denoising network trained solely on this synthetic data is evaluated on real phase maps acquired at 25,000 fps, demonstrating zero-shot generalization to real parallel TIE recordings, with a 13,260% improvement in signal-to-background ratio and 100.8% improvement in jet-region structural sharpness across 20 evaluated frames.

• The paper presents a physics-informed approach using synthetic datasets and a U-Net model to robustly denoise TIE-based phase maps in transient flow imaging.
• Methodology involves emulating experimental artifacts via forward-physical TIE simulation and achieving substantial improvements in PSNR, SBR, and gradient magnitude.
• Experimental results demonstrate strong zero-shot transfer, revealing key flow structures despite overlapping signal and artifact frequencies.

Physics-Informed Synthetic Dataset and Deep Learning Denoising for TIE-Based Phase Mapping in High-Speed Flow Imaging

Introduction

Optical quantitative phase imaging (QPI) serves a central role in the analysis of transient, energetic flow phenomena including compressible gas jets and shockwaves, where rapid refractive index fluctuations encode critical physical diagnostics. The transport-of-intensity equation (TIE), a non-interferometric method, enables QPI under partially coherent illumination and circumvents constraints of interferometric approaches. However, TIE-based phase reconstruction intrinsically suffers from strong, spatially correlated low-frequency artifacts due to inverse Laplacian operations in the reconstruction pipeline. These artifacts critically degrade interpretability, especially when analyzing rapidly evolving, non-repeatable transient flows.

Conventional denoising and post-processing strategies (frequency filtering, Gaussian smoothing, wavelets) fail in this regime since both artifact and signal occupy overlapped frequency bands, and the absence of experimental ground truth precludes direct supervised training. The domain is further challenged by the impossibility of physical replication—no two high-speed frames capture the same flow state. The contribution of this work is a physics-informed synthetic dataset generation pipeline, emulating PTIE experimental artifacts, and a supervised deep learning denoising model with strong zero-shot transfer to real high-speed phase imaging data (2604.10610).

Physics-Informed Synthetic Dataset Design

The dataset construction emulates the entire imaging pipeline, ensuring that both the signal and artifact morphologies match real PTIE recordings. Clean phase distributions are procedurally synthesized using spatial parametric models to capture a diverse set of plausible energetic flow configurations—directly reflecting jet plumes, turbulent eddies, density fronts, expansion fans, and periodic air pocket morphology observed in real flows.

These synthetic phase maps are then subjected to a forward-physical TIE simulation, generating defocused intensity images consistent with the experimental apparatus and introducing measurement noise. Subsequent phase reconstruction is performed using Fourier-domain inverse Laplacian filtering, faithfully replicating the dominant reconstruction artifacts. The dataset comprises 25,000 paired (clean, noisy) 256×256 samples, with sufficient variety to regularize supervised learning over the relevant distribution without overfitting.

Supervised Deep Learning Denoising Pipeline

A compact U-Net-based model, comprising a standard encoder-bottleneck-decoder architecture with skip connections, is optimized to recover artifact-free phase maps from noisy TIE reconstructions. Training is performed exclusively on the synthetic dataset; no experimental data is used in any stage of training or validation. The loss function incorporates pixel-wise L1 error, structural similarity (SSIM) loss, and a weighted MSE emphasizing strong phase gradients, maximizing both global fidelity and flow-relevant structure preservation.

Key architectural choices include limited parameter count (29,777) and batch normalization/dropout regularization, enabling efficient deployment in high-throughput scenarios typical of 25,000 fps flow diagnostics. Optimization uses AdamW and a cosine annealing learning rate schedule, with convergence demonstrated within 20 epochs and no indication of overfitting.

Performance Evaluation and Generalization

Synthetic Domain

On held-out synthetic test data, the network achieves a PSNR of 20.96 dB and MAE of 0.0650, representing a 5.6 dB improvement and 53.7% MAE reduction over initialization, with validation and test set performance nearly identical, demonstrating generalization and resistance to overfit. Qualitative tests confirm effective suppression of structured low-frequency artifacts across diverse morphologies while preserving sharp flow boundaries.

Experimental High-Speed PTIE Data

Critically, the model is evaluated on real experimental PTIE recordings (25,000 fps gas jet flow) in a strict zero-shot manner—every frame is a unique, never-seen physical realization. Post-denoising, structure obscured by strong low-frequency background modulation is successfully revealed, including jet core, nozzle, and parallel flow channels.

Domain-specific, physics-motivated metrics are reported:

• Signal-to-background ratio (SBR): Improved from $0.9438 \pm 0.0322$ to $126.0951 \pm 35.6395$, a 13,260% increase.
• Mean jet-region gradient magnitude: Improved from $0.0738 \pm 0.0124$ to $0.1482 \pm 0.0204$ (100.8% increase).
• Background noise standard deviation: Reduced from $0.0486 \pm 0.0117$ to $0.0044 \pm 0.0036$.

Such improvements are not achievable by frequency-based or classical denoising due to spectral overlap of signal and artifact. Notably, self-supervised frameworks such as Noise2Noise or Noise2Void fundamentally cannot be applied, as the artifact is not pixelwise i.i.d and no repeat realizations are available.

Limitations and Corrective Directions

Systematic domain gap effects were observed:

• Suppression of diffuse outer plumes in the denoised output, traced to the zero-background assumption in synthetic training targets.
• Residual bright spot artifacts at the nozzle, due to a mismatch between synthetic geometry and true experimental nozzle features.

These can be rectified by enriching training data with nonzero backgrounds and improved geometric fidelity, requiring only dataset pipeline modification—no architectural retraining.

Implications and Future Work

The study provides evidence that physics-informed synthetic data, when properly matched to the artifact structure of an imaging pipeline, is an adequate surrogate for unavailable ground truth in high-speed, irreproducible experimental domains. This approach is domain-adaptive and demonstrates strong zero-shot transfer, in line with the effectiveness demonstrated in related physics-informed computational imaging literature.

Practical implications are significant for real-time analysis and scientific understanding of fast-evolving flows, combustion, plasmas, and similar applications where physical repeatability for dataset curation is unattainable. The methodology may be extended to other inverse imaging problems with domain-specific artifacts, given sufficient procedural model fidelity.

Theoretically, embedding physical priors into data generation for supervised learning presents a robust pathway for endowing deep models with inductive bias aligned to real system constraints. This work represents a template for further study in high-speed and fundamentally unsupervised imaging regimes.

Conclusion

A comprehensive synthetic data framework and an efficient deep denoising architecture enable artifact suppression in TIE-based phase maps under high-speed transient flow imaging. The strong zero-shot transfer observed, coupled with explicit domain-specific metric improvements, supports the adoption of physics-informed synthetic training for supervised learning in QPI and analogous inverse-problem domains where paired experimental ground truth is intrinsically inaccessible (2604.10610).